Towards a statistical theory of solid dry friction

TL;DR

This paper develops a statistical model for dry friction that reproduces classical laws and explores how static and dynamic friction depend on surface roughness and velocity.

Contribution

It introduces a microscopic model of dry friction incorporating surface roughness and potential interactions, aligning with Amontons's laws and analyzing velocity dependence.

Findings

Friction force is proportional to normal load N.

Friction force is independent of nominal surface area.

Dynamic friction decays at high velocities and approaches static friction at low velocities.

Abstract

Wearless dry friction of an elastic block of weight N, driven by an external force F over a rigid substrate, is investigated. The slider and substrate surfaces are both microscopically rough, interacting via a repulsive potential that depends on the local overlap. The model reproduces Amontons's laws which state that the friction force is proportional to the normal loading force N and independent of the nominal surface area. In this model, the dynamic friction force decays for large velocities and approaches a finite static friction for small velocities if the surface profiles are self-affine on small length scales.